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1

Turbine wheel reduced modal model for self-excited vibration suppression by inter-blade dry-friction damping

Pešek Luděk, Šnábl Pavel, Prasad Chandra Shekhar

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 6

art. no. e148250

EN

A new approach to calculations based on the modal synthesis method is proposed for the evaluation of structural and dry-friction damping effects on self-excited vibrations due to aeroelastic instability in bladed turbine wheels. The method described herein is used to study dry-friction damping of self-excited vibration of an industrial turbine wheel with 66 blades. For evaluating damping effects, the blade couplings are applied to this particular turbine wheel. Therefore, neighbouring blades are interconnected by rigid arms that are fixed on one side to one blade and are in frictional contact on their free side with the other blade. Due to relatively normal motions in contacts, the prescribed contact forces vary over time. The aerodynamic excitation arises from the spatially periodical flow of steam through the stator blade cascade. In this paper, we attempt to model flow-induced instabilities with the Van der Pol model linked to relative motion between neighbouring blades. The proposed modal synthesis method as ROM is a computationally efficient solution allowing substantial parametrization. The effect of the angles of contact surfaces on the wheel dynamics and on the level of the self-excitation suppression will be discussed herein.

2

Genetic algorithm-PID controller for model order reduction pantographcatenary system

Al-Awad Nasir A., Abboud Izz K., Al-Rawi Muaayed F.

Applied Computer Science

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2021

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Vol. 17, no 2

28--39

EN

Controlling the contact force between the pantograph and the catenary has come to be a requirement for improving the performances and affectivity of high-speed train systems Indeed, these performances can also significantly be decreased due to the fact of the catenary equal stiffness variation. In addition, the contact force can also additionally differ and ought to end up null, which may additionally purpose the loss of contact. Then, in this paper, we current an active manipulate of the minimize order model of pantograph-catenary system. The proposed manipulate approach implements an optimization technique, like particle swarm (PSO), the usage of a frequent approximation of the catenary equal stiffness. All the synthesis steps of the manipulate law are given and a formal evaluation of the closed loop stability indicates an asymptotic monitoring of a nominal steady contact force. Then, the usage of Genetic Algorithm with Proportional-Integral-derivative (G.A-PID) as proposed controller appeared optimum response where, the contacts force consequences to be virtually equal to its steady reference. Finally it seems the advantageous of suggestion approach in contrast with classical manipulate strategies like, Internal mode control(IMC) method, linear quadratic regulator (LQR). The outcomes via the use of MATLAB simulation, suggests (G.A-PID) offers better transient specifications in contrast with classical manipulate.

3

Fuzzy controller of model reduction distillation column with minimal rules

Alawad Nasir, Alseady Afaf

Applied Computer Science

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2020

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Vol. 16, no 2

80--94

EN

In this paper the control of a binary distillation column is described. This control is done with fuzzy logic, one with PI- like fuzzy controller and the other with modified PI fuzzy controller, using the minimal rules for fuzzy processing. This work is focused on model reduction of Wood and Berry binary distillation column to get the best performance. It is desired to minimize the rules in order to reduce the computation time to make a faster decision. Comparisons will be made between two versions of fuzzy controllers utilizing reduced rules to verify the outputs. The controlled variables are top composition with high concentration and bottom composition with low. To demonstrate the performance of the fuzzy PI control schemes, results are compared with a classical PI controller and optimal methods, like Differential Evolution (DE), Invasive Weed Optimization (IWO). The proposed structure is able to quickly track the parameter variation and perform better in load disturbances and also for set point changes. Then all the processes of the distillation column with itۥ s fuzzy controllers are simulated in MATLAB software as the results are shown.

4

Bizon K.

Chemical and Process Engineering

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2015

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Vol. 36, nr 3

365--376

EN

Over the last decades the method of proper orthogonal decomposition (POD) has been successfully employed for reduced order modelling (ROM) in many applications, including distributed parameter models of chemical reactors. Nevertheless, there are still a number of issues that need further investigation. Among them, the policy of the collection of representative ensemble of experimental or simulation data, being a starting and perhaps most crucial point of the POD-based model reduction procedure. This paper summarises the theoretical background of the POD method and briefly discusses the sampling issue. Next, the reduction procedure is applied to an idealised model of circulating fluidised bed combustor (CFBC). Results obtained confirm that a proper choice of the sampling strategy is essential for the modes convergence however, even low number of observations can be sufficient for the determination of the faithful dynamical ROM.

5

The modelling method of discrete-continuous systems

Hein R.

Vibrations in Physical Systems

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2014

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Vol. 26

87--92

EN

The paper introduces a method of discrete-continuous systems modelling. In the proposed method a threedimensional system is divided into finite elements in only two directions, with the third direction remaining continuous. The thus obtained discrete-continuous model is described by a set of partial differential equations. General difference equations of discrete system are obtained using the rigid finite element method. The limit of these equations leads to partial differential equations. The derived equations, expressed in matrix form, allow for the creation of a global matrix for the whole system. The equations are solved using the distributed transfer function method. Proposed approach is illustrated with the example of a simple beam fixed at both ends.

6

Reduction of a vehicle multibody dynamic model using homotopy optimization

Hall A., Uchida T., Loch F., Schmitke C., McPhee J.

Archive of Mechanical Engineering

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2013

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Vol. LX, nr 1

23--35

EN

Despite the ever-increasing computational power of modern processors, the reduction of complex multibody dynamic models remains an important topic of investigation, particularly for design optimization, sensitivity analysis, parameter identification, and controller tuning tasks, which can require hundreds or thousands of simulations. In this work, we first develop a high-fidelity model of a production sports utility vehicle in Adams/Car. Single-link equivalent kinematic quarter-car (SLEKQ, pronounced “sleek”) models for the front and rear suspensions are then developed in MapleSim. To avoid the computational complexity associated with introducing bushings or kinematic loops, all suspension linkages are lumped into a single unsprung mass at each corner of the vehicle. The SLEKQ models are designed to replicate the kinematic behaviour of a full suspension model using lookup tables or polynomial functions, which are obtained from the high-fidelity Adams model in this work. The predictive capability of each SLEKQ model relies on the use of appropriate parameters for the nonlinear spring and damper, which include the stiffness and damping contributions of the bushings, and the unsprung mass. Homotopy optimization is used to identify the parameters that minimize the difference between the responses of the Adams and MapleSim models. Finally, the SLEKQ models are assembled to construct a reduced 10-degree-of-freedom model of the full vehicle, the dynamic performance of which is validated against that of the high-fidelity Adams model using four-post heave and pitch tests.

PL

Pomimo stale rosnącej mocy obliczeniowej współczesnych procesorów, redukcja złożonych, wieloczłonowych modeli dynamicznych pozostaje ważnym tematem badań, zwłaszcza dla optymalizacji projektowania, analizy wrażliwości, identyfikacji parametrów i optymalizacji sterowników, które mogą wymagać setek lub tysięcy symulacji. W pierwszej części pracy autorzy przedstawiają model o wysokiej wierności opracowany dla seryjnie produkowanego samochodu sportowo-użytkowego (SUV) przy pomocy oprogramowania Adams/Car (MSC.Software Corporation). Następnie w środowisku MapleSim (Waterloo Maple Inc.) zostały opracowane równoważne ćwiartkowe (quarter-car) modele kinematyczne o jednym połączeniu, typu SLEKQ, dla zawieszenia przedniego i tylnego. By uniknąć komplikacji obliczeniowych związanych z wprowadzeniem tulejowania lub pętli kinematycznych, wszystkie układy przenoszące zawieszenia zostały zastąpione pojedynczymi skupionymi nieresorowanymi masami w każdym rogu pojazdu. Zaprojektowane modele typu SLEKQ odtwarzają właściwości kinematyczne modelu kompletnego zawieszenia wykorzystując przy tym tablice przeglądowe lub funkcje wielomianowe, które zostały wcześniej wyznaczone za pomocą wysokiej wierności modelu typu Adams. Zdolność predykcyjna każdego modelu SLEKQ zależy od użycia właściwych parametrów opisujących nieliniowe sprężyny i amortyzatory, które uwzględniają sztywność i wpływ na tłumienie drgań wnoszony przez tulejowanie i nieresorowane masy. Optymalizację homotopową zastosowano w celu identyfikacji tych parametrów, które minimalizują różnice między odpowiedziami uzyskanymi w modelach typu Adams i SLEKQ. Ostatecznie, z modeli SLEKQ zostaje złożony zredukowany model o dziesięciu stopniach swobody reprezentujący cały pojazd. Właściwości dynamiczne tego modelu są poddane walidacji przez porównanie z właściwościami wysokiej wierności modelu typu Adams w czterokolumnowych testach kołysania i pochylania.

7

Assessment of parameters of laboratory model of telecommunication mast

Snamina J., Orkisz P.

Mechanics and Control

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2011

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Vol. 30, no. 3

170-175

EN

This work presents an algorithm for determining values of parameters of a laboratory model of a telecommunication mast. The algorithm is constituted by several steps finally leading to a physically executable model, being a good representation of the dynamics of the mast construction. The calculations carried out were used for design a laboratory model of a telecommunications mast.

PL

W pracy przedstawiono algorytm wyznaczania wartości parametrów laboratoryjnego modelu masztu telekomunikacyjnego. Algorytm składa się z kilku kroków, w wyniku których uzyskano fizycznie realizowalny model. Otrzymany model dobrze odwzorowuje dynamikę konstrukcji masztu. Przeprowadzone obliczenia wykorzystano do zaprojektowania modelu laboratoryjnego masztu telekomunikacyjnego.

8

Hybrid reduced model of continuous system

Hein R., Orlikowski C.

Vibrations in Physical Systems

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2010

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Vol. 24

143--149

EN

The paper introduces an alternative method of modelling and modal reduction of continuous systems. Presented method is a hybrid one. It combines the advantages of modal decomposition method and the rigid finite element method. In the proposed method continuous structure is divided into one-dimensional continuous elements. For each 1D element modal decomposition and reduction is applied. Interactions between substructures are described by lumping techniques. Presented method enables to obtain reduced, low order modal model of considered system. The proposed approach is illustrated by selected examples.

PL

W artykule przedstawiono alternatywną metodę modelowania i modalnej redukcji układów ciągłych. Zaprezentowana metoda jest metodą hybrydową. Łączy zalety metod dekompozycji modalnej i sztywnych elementów skończonych. W proponowanej metodzie układ ciągły dzielony jest na jednowymiarowe podukłady ciągłe. Dla każdego podukładu jednowymiarowego budowany jest modalny model zredukowany. Poszczególne modele zredukowane wiąże się ze sobą poprzez oddziaływania między nimi modelowane za pomocą metody sztywnych elementów skończonych. Zaprezentowana metoda umożliwia otrzymanie zredukowanego modelu modalnego niskiego rzędu. Proponowane podejście jest zilustrowane prostymi przykładami.

9

Problemy redukcji złożonych modeli obiektów sterowania

Rydel M., Stanisławski W.

Pomiary Automatyka Kontrola

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2010

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R. 56, nr 2

197-200

PL

W artykule zaprezentowano zagadnienia związane z redukcją złożonych modeli obiektów sterowania. Przedstawiono podstawowe grupy metod redukcji wraz z omówieniem ich wad i zalet dla celów redukcji złożonych modeli obiektów sterowania. Zaproponowano wprowadzenie nowej miary błędu aproksymacji dla oceny dokładności aproksymacji modelu zredukowanego. Dobór parametrów metod redukcji pod kątem minimalizacji tej miary błędu umożliwia uzyskanego znacznie lepszych rezultatów redukcji niż minimalizacja normy Hankela błędu aproksymacji.

EN

Model order reduction problems of complex control model are presented in this paper. The article presents basic method group of complex control models reduction. Out of the many methods known from the literature, the methods based on balancing a system and then reducing it (SVD method) have become of great significance [1, 2, 5, 6, 10, 11, 13, 17, 23]. Also Krylov-based approximation methods are widely used, which are based on moment matching of the impulse response of the reduced system [1-3, 7, 9, 20]. Most of the MIMO models are characterized by large differences in gain characteristic and gain variability in frequency function (Fig. 1). The Hankel norm of approximation error (4) can't be used to estimate quality of approximation gain characteristic (Fig. 2). Authors propose in the paper new approximation error measure for reduced models of control objects (5). Minimizing this approximation error for selection of method reduction parameters gives better results than minimizing Hankel norm of approximation error (Tab. 1, Fig. 2). The reduction results of a structural model of component 1r (Russian service module) of the International Space Station [4] are also described in the paper [4].